Error estimate and stability for the finite volume method of the convection-diffusion problem

Abstract EN

In this paper, a finite volume method is studied for two-dimensional linear convection-diffusion problem.

A linear convection term is approximated by upwind finite element scheme considered over a mesh to the triangular grid, whereas the diffusion term is approximated by using divergence theorem and approximate the direction derivative by difference quotient.

The stability and error estimate of this method are proved under some assumption on the numerical fluxes.